For more than 150 years (e.g. see Pachl [1]) railways have been very traditional when it came to the safety principles that they applied. Nevertheless, railway safety has become increasingly innovative over the last decades. This started with electronic interlockings that required a new type of standard, such as EN 50716 [2] and EN 50129 [3]. This has led to a completely new approach to assessing whether an electronic device is safe, i.e. the safety assessment. New developments such as automatic underground railways, Automatic Train Operation (ATO), the Hyperloop (a Maglev train running in a low-pressure tube), the use of hydrogen as fuel, the implementation of artificial intelligence, as well as the increasing importance of cybersecurity all require further development of the safety assessment methods. In this paper, an approach to railway system safety with innovative technology is shown and the challenges connected with the safety assessment are discussed.

Aim. To identify acceptable fail-safety architectures for critical high-speed rail systems, as well as their capabilities and limitations. Methods. Construction and study of several mathematical models of system dependability and functional safety. Selection of acceptable faail-safety architectures for critical high-speed rail systems. Results. An analytical and numerical analysis of the dependability of the widely used 2oo3 safety architecture has shown that majority logic can significantly improve the reliability of the results (mean time to functional failure of a majority system is twice that of the original object). However, the system’s dependability, and, consequently, its fail-safety, is lower than that of the original object. Therefore, such an architecture is not acceptable beyond SIL3. For the purpose of ensuring this level of fail-safety, the alternative (1oo2)P architecture may prove to be preferable as it lacks restoring organs and switching devices. It is made of two components that operate in parallel, each of which uses a hot standby setup. However, one should not forget that such systems are prone to false alarms. It has been shown that hybrid majority architectures (2oo3)P or 2oo4 can provide SIL4 fail-safety. However, it should be noted that a significant portion of the majority setups that ensure fail-safety of critical systems are switching circuits designed for disconnecting failed components and activating backup components. This circumstance affects the effectiveness of majority redundancy, as it requires the use of additional tools and procedures. This shortcoming is due to the fact that in both hardware and software implementations, the fault masking mechanism, i.e., voting, faulty channel identification, blocking thereof, and then resuming normal operation, is repeated in every system cycle, regardless of the presence or absence of faults. Practically, the associated time losses are as high as 30 to 50%. The disadvantages of majority redundancy also include the large number of connections between channels and certain design difficulties. These limitations have a negative, but not decisive, effect on the selection of an acceptable fail-safety architecture. They should be taken into account given each specific object and its operating conditions.

The paper aims to analytically assess the reliability of energy transmission through the electric grid of PAO Rosseti Tsentr. The study describes the company’s structure and provides a detailed balance of electric energy transmission through the company’s grid and from the grid to the consumers. The shortcomings of the company’s reporting activities are noted. Based on publicly available information, the authors analysed the accidents that affected the company’s grid within the addressed period of time while noting the specificity of energy transmission in each of the company’s branches. The concept of specific accident rate is introduced to define the rate of adopted emergency measures that have been developed by each company to reduce the undersupply of electric energy caused by emergency shutdowns. The main causes of failures were analysed. As a result, it was established that the main causes are the effects of repeated natural phenomena, as well as untimely maintenance of electrical installations. The authors primarily used the methods of numerical analysis, as well as general scientific methods of information processing. The analysed materials were visualised in the form of MATLAB diagrams. The results of the study may be of interest to technical specialists of the PAO ROSSETI electric grid companies, as well as researchers who specialise in power supply reliability.

Aim. The paper examines the matter of accounting for the effect of climate change on the functional reliability of regional road networks. An algorithm and method for assessing the functional reliability of a road are proposed that are based on assessing the durability and residual life of the road surface structure according to deformation criteria: (1) the maximum permissible residual deflection of the road surface, (2) the decrease of the deformation modulus of the road surface material as a result of multiple elastic-plastic deformation of the road surface caused by traffic, (3) the emergence of unacceptable longitudinal potholes. Methods. The mathematical model of a road network in the form of a Bayesian network allows simulating (1) climate/weather conditions, (2) real-time traffic following an accident using an agent-based model that uses traffic information accumulated through continuous monitoring (including surveillance cameras and drones), travel time of each vehicle, and traffic volume on each road. For the purpose of identifying the probability of failure of each section of the road network, a method was developed for determining the initial reliability that takes into account the effect of various factors of destruction of the road surface structure. The reliability of the selected transport network and the PoF of each of its sections were calculated using a Bayesian network, and the residual life of each road section was calculated based on deformation criteria. Results. A comparative analysis of the vulnerability of the road network of the Yekaterinburg-Tyumen route (Ural Federal District) for both passenger and freight transport was conducted, both taking into account the climate trends of the Middle Urals and otherwise, using the example of a traffic accident that resulted in a partial destruction of a single bridge and a redistribution of traffic flows. The identified residual life, the probability of failure-free operation and the reliability of each section of the road network allowed identifying the most vulnerable sections of the road networks of the Ural Federal District, as well as the scope of necessary repair activities. Conclusion. The application of the developed method also showed that the functional reliability of the Yekaterinburg-Tyumen route for regular transport is 99.55% and 98.47% for vehicles with a carrying capacity of over 20 tons. The use of an agent-based model of driver behaviour to assess and analyse the vulnerability of the Yekaterinburg-Tyumen transport network in the event of a bridge failure showed that the extension of the route due to a bridge failure leads to an increase in the carbon footprint of the road network and a negative impact on the environment.

This article generalizes fundamental research devoted to a class of probability distributions known as Almost Lack of Memory (ALM) distributions. While the classical exponential distribution is uniquely characterized by the lack of memory property at any age, ALM distributions exhibit this property selectively, at ages forming a discrete sequence {0,  c, 2c, ...} for a positive constant c. This generalization provides a powerful and versatile tool for modeling lifetimes, times to failure, and waiting times under periodic, non-stationary conditions. We present a comprehensive characterization of ALM distributions through several equivalent properties: a specific analytical form of the distribution function, a periodic failure rate, and a probabilistic representation in which a random variable decomposes into the sum of a component truncated on [0, c) and a geometrically distributed component scaled by c. This decomposition is of key importance for both theoretical analysis and practical applications. The intrinsic connection between ALM distributions and periodic non-homogeneous Poisson processes is rigorously established. Furthermore, the article discusses important statistical aspects, including parameter estimation by maximum likelihood and method of moments, as well as hypothesis testing for model discrimination. The applicability of ALM theory is demonstrated in various fields, including the reliability of technical systems operating under cyclic loads, insurance for modeling losses with a seasonal structure, and environmental sciences for studying phenomena driven by periodic forces. Bridging the gap between theoretical probability and the need for modeling real-world periodicity, ALM distributions offer a robust and mathematically elegant tool for analysis under non-stationary conditions.

Aim.  The paper aims to supplement certain aspects of the Fault Tree Analysis (FTA) methodology. Assuming that the input data, namely the failure rates of basic events, are random variables, an uncertainty analysis of the dependability indicator at the top event of the fault tree (FT) is usually performed. However, if the dependability indicator of the FT top event is random, then the decision on whether the requirements of the technical specifications (TS) are met should not be made by simply comparing the calculated indicator with the requirement. One of the goals in this situation is to construct decision-making criteria for the fulfillment of TS requirements using statistical hypothesis testing methods. If the uncertainty of the input data is modeled using a lognormal distribution, the choice of the error factor (EF) is often unjustified. The second objective of this paper is to provide a justification for the choice of EF. The ultimate goal is to introduce additional sensitivity measures in situations where the reliability indicators of interest for the FT top event are not the failure probability or unavailability, but the failure flow or mean time between failures.  Methods.  Classical methods of probability theory, mathematical statistics, and mathematical reliability theory are used.  Conclusions.  The paper shows that decision-making on the fulfillment (or nonfulfillment) of TS requirements, in cases where the input data (failure rates) have statistical uncertainty, should be based on statistical hypothesis testing methods, namely hypothesis testing using confidence intervals. Furthermore, in case of a lognormal distribution of failure rates, a justification for the choice of the error factor (EF) is provided. If the TS requirements concern the failure flow or the mean time between failures, and the sensitivity of the FT top event dependability indicator with respect to basic events is being investigated, then special sensitivity measures must be used.

Aim. Unmanned aerial vehicles (UAVs) are increasingly integrated into intelligent transportation systems (ITS), becoming one of the critical elements of the transportation infrastructure. At the same time, the dependence of UAVs on software, wireless communication channels, and external navigation systems makes them vulnerable to cybersecurity threats. The purpose of the paper is to conduct a comprehensive analysis of cybersecurity threats to UAVs in the context of their operation as part of ITS and to develop a threat model covering hardware, software, communication, and infrastructure components. Methods. The paper uses methods of system analysis, cybersecurity threat modelling, as well as architecture analysis of UAV software and hardware systems involving the identification of key targets. The paper uses methods based on the classification of threats according to the standards of the FSTEC of the Russian Federation, as well as methods for analysing the relationships between threats, vulnerabilities, and means of protection. Results. A threat model of UAVs as an element of ITS has been developed, covering hardware components, software, communication channels, information flows, and ground infrastructure. The most critical threats have been identified, including disruption, data compromise, and physical impact. An analysis of existing information security solutions has been carried out and it has been shown that there is no systematic approach to ensuring security. Based on the analysis, the authors substantiate the application of the security by design (SBD) methodology according to GOST R 72118-2025. Conclusion. The proposed SBD-based approach allows designing UAVs with inherent resistance to a wide range of cybersecurity threats, including cyber-physical attacks and data integrity violations, which is especially important given the requirements of UAV integration into ITS, where the failure or compromise of an element can lead to system failures. Experimental testing of the approach as part of educational projects confirms the applicability and effectiveness of the SBD methodology.

The paper addresses the problem of integrating computer-based railway signalling systems with supervisory control and data acquisition (SCADA) systems. Conventional network protocols with flat memory addressing create a semantic gap between physical equipment and traffic control abstractions, which exponentially increases the algorithmic complexity of configuration and diminishes cyber-physical security. The aim of the study is to develop a domain-specific information model for basic trackside assets (railway switch, route section, signal) based on the IEC 62541 (OPC UA) standard. The paper proposes a method for encapsulating the fail-safe interlocking logic directly into the protocol’s network stack using software calls (methods) and dynamic management of the execution permission system attribute. It is mathematically proven that applying property inheritance and machine selfdescription mechanisms allows reducing the algorithmic complexity of operator workstation configuration from a linear-multiplicative dimension of O(N×M) to O(N). The findings confirm an improved system protection against logical attacks and operator errors. The proposed data type hierarchy can serve as a prototype for creating a single industry specification for the interaction of railway signalling systems.

The article presents a comprehensive structural and functional model of Internet segmentation that identifies three distinct layers: the Surface Web, the Deep Web, and the Dark Web. The scientific novelty lies in the definition and solution of a scientific problem consisting in the mathematical formalisation of the model, including structural analysis using graph schemes and functional analysis with input/output data and processing functions. The authors propose a multi-level framework for assessing cyber risks at the intersection of artificial intelligence technologies (AI) and cybercrime, as well as a mathematical risk calculation model. The threats of the shadow segment are classified, and a hierarchical model of protective measures adapted to counter AI-enhanced threats is developed. The model is formalised as a directed graph with data aggregation and risk assessment functions, enabling quantitative vulnerability analysis.